## Sarin learns lines and angles in school (Math Concept)

Lines

Angles

When two straight lines meet or intersecting each other, they form angles.

Two straight lines can only intersect at one point.

To measure angles

The unit of measurement for angle is degree. Symbol: ^{0}

Examples:

90 degree, 90^{0}, 30^{0}, 45^{0}, 120^{0}, 180^{0}, 270^{0}, 360^{0} etc……

Angles are the measurement of two lines at their intersection point. It is the separation between the two lines that from a reference point.

A protractor is a tool to use for measuring angles.

The angle is 60^{0} measured using a protractor.

A normal protractor can measure angle from 0^{0 }to 180^{0}.

What is the angle measure on a straight line?

A circular protractor measure angle from 0^{0 }to 360^{0}

The angle indicate in the diagram is 300^{0}

So, a straight line can also measure 360^{0},

and it is depends on how the rotation direction indicated.

Different type of angles

An acute angle is an angle measuring between 0 and 90 degrees.

A right angle is an angle measuring 90 degrees.

An obtuse angle is an angle measuring between 90 and 180 degrees.

A reflex angle is an angle measuring greater than 180 degrees.

A straight angle is an angle measuring 180 degrees.

An acute angle or an obtuse angle, with their respective reflex angles measuring 360^{0}.

Two angles are called complementary angles mean the two angles add up gives 90 degrees, or form a right angle.

30^{0} + 60^{0} = 90^{0} which is right angle

30^{0} is complement angle of 60^{0}, or

angle 60^{0} is complement of angle 30^{0}

Two angles are called supplementary angles mean the two angles sum up gives 180^{0}, or form a straight angle (line).

120^{0} + 60^{0} = 180^{0}

Angle 120^{0} is supplement of angle 60^{0}

Perpendicular lines

When two lines intersect or meet with an angle measuring 90^{0} or form a right angle, we call the two lines the perpendicular lines.

Line CD meet Line AB at point D

perpendicularly.

Angle ADC = Angle CDB = 90^{0}

Line CD intersect Line AB at point E

Perpendicularly.

Angle AEC = Angle CEB = 90^{0}

Angle AED = Angle DEB = 90^{0}

Vertical angles

If line CD intersects line AB at point E as below, the angle AED measures the same as angle CEB. There are vertical angles.

Same for angle AEC and angle DEB,

angle AEC = angle DEB and there are vertical

angles

Parallel lines

Line AB is said parallel to line CD, if the shorter distance between them is equal as below diagram shown.

The shorter distance is the perpendicular line

that meet line AB and line CD

Line blue, line red and line green

are parallel lines.

Dotted line is perpendicular to all three lines

Follow the above diagram,

Line 3 is perpendicular to line 1 and line 2. So line 1 is parallel to line 2.

As line 4 intersect both line 1 and line 2,

we have angle c = angle g and there are corresponding angles.

Similarly,

angle a = angle e and there are corresponding angles.

angle j = angle p and there are corresponding angles. Etc….

Since angle g and angle m are vertical angles,

Angle c = angle m, and there are call alternate interior angles

Similarly, angle j = angle e, and there are call alternate interior angles.

You can also see that,

angle j + angle m = 180^{0}, angle c + angle e = 180^{0}, ext….

angle a = angle p, and there are call alternate exterior angles. Ext….

With another line 5 parallel with line 4 intersectingline 1 and line 2,

you can work out that,

Angle j = angle k, angle n = angle m

Also angle j + angle d + angle m + angle f = 360^{0} etc….

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